Solve. Round your answer to the nearest thousandth. 4^x = 5 x = ____

Apply Logarithm: 4^x = 5 Apply the logarithm to both sides of the equation to solve for x. log(4^x) = log(5)Use Power Property: log(4^x) = log(5) Use the power property of logarithms to bring the exponent x in front of the log. x * log(4) = log(5)Isolate x: x * log(4) = log(5) Isolate x by dividing both sides of the equation by log(4). x = log(5) / log(4)Calculate Value: Calculate the value of x using a calculator. x = log(5) / log(4) x ≈ 1.16096404744... Round the answer to the nearest thousandth. x ≈ 1.161

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve. Round your answer to the nearest thousandth. $\newline$ $4^x = 5$ $\newline$ $x =$ ____

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using common logarithms

Full solution

Q. Solve. Round your answer to the nearest thousandth.

\newline

4^x = 5

\newline

x =

____

Apply Logarithm: $4^x = 5$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $log(4^x) = log(5)$
Use Power Property: $\log(4^x) = \log(5)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(4) = \log(5)$
Isolate $x$ : $x \cdot \log(4) = \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(4)$ . $\newline$ $x = \frac{\log(5)}{\log(4)}$
Calculate Value: Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(5)}{\log(4)}$ $\newline$ $x \approx 1.16096404744\ldots$ $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 1.161$